Exploring localized ENZ resonances and their role in superscattering, wideband invisibility, and tunable scattering

While the role and manifestations of the localized surface plasmon resonances (LSPRs) in anomalous scattering, like superscattering and invisibility, are quite well explored, the existence, appearance, and possible contribution of localized epsilon-near-zero (ENZ) resonances still invoke careful exploration. In this paper, that is done along with a comparison of the resonances of two types in the case of thin-wall cylinders made of lossy and loss-compensated dispersive materials. It is shown that the localized ENZ resonances exist and appear very close to the zero-permittivity regime, i.e., at near-zero but yet negative permittivity that is similar to the ENZ modes in thin planar films. Near- and far-field characteristics of the superscattering modes are investigated. The results indicate that the scattering regimes arising due to LSPRs and localized ENZ resonances are distinguishable in terms of the basic field features inside and around the scatterer and differ in their contribution to the resulting scattering mechanism, e.g., in terms of the occupied frequency and permittivity ranges as well as the sensitivity to the wall thickness variations. When the losses are either weak or tend to zero due to the doping with gain enabling impurities, the sharp peaks of the scattering cross-section that are yielded by the resonances can be said to be embedded into the otherwise wide invisibility range. In the case of lossy material, a wide and continuous invisibility range is shown to appear not only due to a small total volume of the scatterer in the nonresonant regime, but also because high-Q superscattering modes are suppressed by the losses. For numerical demonstration, indium antimonide, a natural lossy material, and a hypothetical, properly doped material with the same real part of the permittivity but lower or zero losses are considered. In the latter case, variations of permittivity with a control parameter can be adjusted in such a way that transitions from one superscattering mode to another can be achieved. In turn, transition from the strong-scattering to the invisibility regime is possible even for the original lossy material. The basic properties of the studied superscattering modes may be replicable in artificial structures comprising natural low-loss materials.

In order to confirm that the features observed in Figs. 1, 2, 4 and 9 have regular, not accident nature, the numerical study has been carried out for multiple sets of a and b.The selected results are presented in Figs.S1-S5. Figure S1 shows t vs. ka for the case of a=28m and a=42m; compare to t is weakly sensitive to the applied variations of C. The aforementioned features can be explained in terms of dark and bright modes, but this is beyond the scope.The situation is similar for the modes of the type A (not shown).For instance, for the maximum of t at ka=0.633, C=0.5 (and even a larger C) can be sufficient to see the effect of this mode in t, while C=0.002 warranties that it is seen almost to the same extent as for C=0.In turn, the mode arising at ka=0.6595 shows max t >2.5 for C=0.002 and max t >1 for C=0, whereas max t <0.5 for C=0.005, 0.025, and 0.05.For the sake of completeness, we present the results for the gain case, i.e., Im c is assumed to have the opposite sign than above.In Fig. S4, t vs. ka is presented for the selected values of C, for one of the modes of the type B (vicinity of ka=0.716) and one of the modes of the type A (vicinity of ka=0.633).
For the former, we observe the increase of t up to 6.8 when C=-0.05.The possibility of a sharp increase of t is expected to occur in the close vicinity of the complex eigenvalues; it needs an additional study.Notably, such a behavior has been observed for the other mode of the type B (in the vicinity of ka=0.713).In this case, max t>14 is obtained C=-0.025 (not shown), assuming that C takes the same values as in Fig. S4.In case of the lowest-frequency mode which has the lowest Q-factor among the studied modes, there is just a weak effect of C variable from 0 to -0.05, as in Fig. S4 (not shown).However, even for this mode larger max t can be achieved.In particular, max t>11 has been obtained in the simulations at C=-1.5.In line with the expectations of the effects of complex eigenvalues, we performed simulations in the vicinity of ka=0.633(mode of the type A) and ka= 0.716 (mode of type B).The results obtained for the former show that max t>29 when C=-0.1.At the same time, much smaller values of max t are obtained when C=-1.0, -0.7, -0.5, and -0.2, so the optimum C does exist.For the latter, max t>35 when C=-0.1, and then it becomes when t takes the same values as above, i.e., from -1.0 to -0.2.Finally, in Fig. S5, the numerical results are presented for t in (ka,T)-plane for a thinner-wall cylinder than in Fig. 9.The results indicate that no new feature appears when b=11 mm is changed for b=13 mm.The only significant difference is the slope of the "mountain" of max t.Indeed, the slope in Fig. S5 is larger than that in Fig. 9(a) but similar to that in Fig. 9(b).This means that the same increments T lead to either smaller or larger changes in spectral location of max t, depending on b/a

Fig. 1 .
Fig. 1.As seen, increase of a and, generally speaking, increase of the volume of the scatterer, lead to that the weak scattering occurs only in the vicinity of Re c=1, whereas the signatures of the modes of type A and B (which are suppressed here by losses) are seen in the presented results.The effect of LSPRs (both the lowest-frequency mode and the modes referred to as the modes of the type A) in strong scattering is dominant at Re c<0 in all cases, what leads to that the smaller b/a is, the larger t can be achieved.Vice versa, at Re c>1, the larger structure's volume is the dominant factor for obtaining a larger t.It follows from the obtained results that smaller a and larger b/a yield a wide invisibility range, while strong scattering at Re c<0 does remain.

Figure S2 .
Figure S2.Normalized total scattering cross section, t, for thin-wall cylinders made of dispersive material with c=Re s for b=27 m (black dotted line), 26 m (red dashed line), and 25 m (blue solid line), a=28 mm; the ratios of b/a are shown near the curves.
Figure S4.Normalized total scattering cross section, t, at selected values of C in Im c=C Im s, (a) C=0 (blue solid line), -0.002 (red dashed line), -0.005 (green dash-dotted line), -0.025 (black dotted line), and -0.05 (light-blue dashed line), for one of the modes of type B; (b) same but for one of the modes of type A; b=11 m and a=14 m.
Figure S5.Normalized total scattering cross section, t, in (ka,T)-plane for b=13 m and a=14 m, (a) c=s, (b) c=Re s .